Intro

Background Information: We were tasked by Kirk Bogard, the Associate Vice President for Development and External Relations at Miami University to explore a dataset of real student data in order to find relationships and patterns that he can use to give Miami a competitive advantage. After exploring the data, we found a few particular variables that can help us find a potential relationship in the dataset, survey_salary, survery_internships, and survey_state. We plan to build a regression model using the number of internships during college to predict salary after graduation, using state to control for salary. The purpose of this analysis is to provide information on the relationship between number of internships and salary information to FSB Career Services. This will help them give more accurate guidance to students to ensure they get the best full time opportunity for them.

Survey Overview: Usable Response %: Our initial dataset included information on much more than just internship and salary information, and as such there were observations that provided no meaningful information to our model. After removing these observations (e.g. those without a reported salary after graduation, unreported number of internships, unreported starting location), the dataset shrunk to a bit over 50% of the original size. Out of 3235 original observations, we were left with little over 1700 to work with.

Distribution of Number of Internships: To understand the data a bit better, we wanted to explore how many internships students were completing before going into the job force. According to this basic histogram, most students completed 1 or 2 internships, followed by 3, while 0,4, and 5 had fairly few instances. The distribution looks relatively normal, but seems to be skewed slightly right.

Internship Effects on Salary: Mean Salary by Number of Internships: This is a bar chart depicting the average salary after graduation grouped by the number of internships they completed. What we see from this graph is that salary increases a bit for each additional internship completed up to 3 internships, after which average salary levels out. We expected salary to generally increase after an additional internship is completed, and the chart seems to support this. However, it is interesting to see that having additional internships after completing 3 does not seem to have an effect on salary, even lowering expected salary with 5 internships (potentially due to there being so few observations with 5 internships). This could indicate you do not need more than 3 internships if you want to maximize salary after graduation.

Regression Model Predicting Salary by Number of Internships:

Using a regression model we predicted salary by number of internships using 0 internships as a baseline.

There is a sizable increase in salary when adding another internship up until 3 internships, 4 internships is a slight decrease from 3 internships and 5 internships is about the same as 3 and 4, but it is not a significant predictor.

Survey Overview

Overview of survey responses

row

Usable Response %

Usable Responses

1725

row

Distribution of Number of Internships

Internship Effects on Salary

Column

Mean Salary by Number of Internships

Column

Regression Model Predicting Salary by Control Variables


Call:
lm(formula = formula_control, data = df)

Residuals:
   Min     1Q Median     3Q    Max 
-38747  -6310   -332   5899 108835 

Coefficients:
                                                Estimate Std. Error t value
(Intercept)                                    49588.280   8391.856   5.909
survey_stateIL                                  4122.531    646.687   6.375
survey_stateOther                               4455.649    654.219   6.811
survey_stateUnknown                             3359.317   1364.012   2.463
major1Business Analytics                        6636.994   2011.416   3.300
major1Business Economics                        3170.312   1453.012   2.182
major1Entrepreneurship                         -5333.738   3238.323  -1.647
major1Finance                                   3389.686    885.634   3.827
major1Human Capital Mgmt& Leadership           -4247.507   1851.485  -2.294
major1Information Systems                       7599.443   1376.562   5.521
major1Management and Leadership                -3130.762   2119.192  -1.477
major1Marketing                                -5459.029    940.453  -5.805
major1Supply Chain & Operations Mgmt              47.551   1151.406   0.041
`Combined Bacc and Masters`                     -971.754   1169.298  -0.831
`Dean's List`                                   -748.616    696.333  -1.075
`First Generation College Stdnt`                -843.117   1025.153  -0.822
`FSB Scholars`                                   934.737   1759.242   0.531
`Honors Program`                                1279.472   1897.256   0.674
`President's List`                                67.974   1365.768   0.050
`Cum Laude`                                     4721.870   2395.703   1.971
`Magna Cum Laude`                               6037.442   2572.600   2.347
`Summa Cum Laude`                               9135.325   2730.274   3.346
`University Honors`                             -767.161   2072.027  -0.370
`UniversityHonors w/Distinction`               -1855.295   3917.603  -0.474
minor1Arts Related                             -5919.015   2248.640  -2.632
minor1Business Analytics                        -990.745   1960.587  -0.505
minor1Business Legal Studies                   -5270.065   5683.975  -0.927
minor1Economics                                -3898.320   2835.311  -1.375
minor1Education                                -6048.032   7830.299  -0.772
minor1Engineering/Science                        626.980   2709.195   0.231
minor1Entrepreneurship                           499.853   2596.750   0.192
minor1Health Related                          -10084.253  11047.638  -0.913
minor1Humanities                               -1173.819   2017.328  -0.582
minor1Information Security                      1386.937   3335.584   0.416
minor1Information Systems                       1105.064   2158.897   0.512
minor1Interactive Media Studies                    8.363   2258.877   0.004
minor1International Business                   -2974.845   3593.633  -0.828
minor1Language                                 -2337.604   2129.496  -1.098
minor1Mangement and Leadership                 -1689.472   2204.826  -0.766
minor1Marketing                                -2331.236   2822.045  -0.826
minor1Math/Stat                                  -30.826   4091.193  -0.008
minor1Media Related                             1702.977   4238.460   0.402
minor1No Minor                                  -974.393   1783.141  -0.546
minor1Political Science                         2119.806   3073.955   0.690
minor1Sport Management                         -2486.016   2510.684  -0.990
minor1Supply Chain Management                   -501.174   2535.387  -0.198
IPEDS.Race.EthnicityAsian                      -1425.230   7788.050  -0.183
IPEDS.Race.EthnicityBlack or African American   3445.704   8001.449   0.431
IPEDS.Race.EthnicityHispanic/Latino            -1987.979   7730.110  -0.257
IPEDS.Race.EthnicityMulti Racial               -2349.612   7773.044  -0.302
IPEDS.Race.EthnicityNon-Resident Alien         -3831.434   7974.649  -0.480
IPEDS.Race.EthnicityUnknown                    -1256.635   9373.964  -0.134
IPEDS.Race.EthnicityWhite                      -3604.573   7631.910  -0.472
GenderMale                                      -453.290    579.518  -0.782
GPA.Range2.50 - 2.99                            5074.447   2944.495   1.723
GPA.Range3.00 - 3.49                            9010.521   2841.992   3.170
GPA.Range3.50 - 4.00                            8059.228   3755.374   2.146
                                              Pr(>|t|)    
(Intercept)                                   4.16e-09 ***
survey_stateIL                                2.36e-10 ***
survey_stateOther                             1.35e-11 ***
survey_stateUnknown                           0.013885 *  
major1Business Analytics                      0.000988 ***
major1Business Economics                      0.029257 *  
major1Entrepreneurship                        0.099732 .  
major1Finance                                 0.000134 ***
major1Human Capital Mgmt& Leadership          0.021908 *  
major1Information Systems                     3.91e-08 ***
major1Management and Leadership               0.139774    
major1Marketing                               7.70e-09 ***
major1Supply Chain & Operations Mgmt          0.967063    
`Combined Bacc and Masters`                   0.406060    
`Dean's List`                                 0.282493    
`First Generation College Stdnt`              0.410950    
`FSB Scholars`                                0.595261    
`Honors Program`                              0.500163    
`President's List`                            0.960312    
`Cum Laude`                                   0.048892 *  
`Magna Cum Laude`                             0.019051 *  
`Summa Cum Laude`                             0.000838 ***
`University Honors`                           0.711246    
`UniversityHonors w/Distinction`              0.635862    
minor1Arts Related                            0.008560 ** 
minor1Business Analytics                      0.613393    
minor1Business Legal Studies                  0.353967    
minor1Economics                               0.169342    
minor1Education                               0.439994    
minor1Engineering/Science                     0.817012    
minor1Entrepreneurship                        0.847380    
minor1Health Related                          0.361481    
minor1Humanities                              0.560734    
minor1Information Security                    0.677610    
minor1Information Systems                     0.608813    
minor1Interactive Media Studies               0.997047    
minor1International Business                  0.407897    
minor1Language                                0.272482    
minor1Mangement and Leadership                0.443629    
minor1Marketing                               0.408877    
minor1Math/Stat                               0.993989    
minor1Media Related                           0.687889    
minor1No Minor                                0.584831    
minor1Political Science                       0.490540    
minor1Sport Management                        0.322232    
minor1Supply Chain Management                 0.843326    
IPEDS.Race.EthnicityAsian                     0.854819    
IPEDS.Race.EthnicityBlack or African American 0.666789    
IPEDS.Race.EthnicityHispanic/Latino           0.797077    
IPEDS.Race.EthnicityMulti Racial              0.762479    
IPEDS.Race.EthnicityNon-Resident Alien        0.630969    
IPEDS.Race.EthnicityUnknown                   0.893375    
IPEDS.Race.EthnicityWhite                     0.636772    
GenderMale                                    0.434218    
GPA.Range2.50 - 2.99                          0.085007 .  
GPA.Range3.00 - 3.49                          0.001549 ** 
GPA.Range3.50 - 4.00                          0.032013 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 10740 on 1668 degrees of freedom
Multiple R-squared:  0.2218,    Adjusted R-squared:  0.1957 
F-statistic: 8.491 on 56 and 1668 DF,  p-value: < 2.2e-16

Column

Regression Model Predicting Salary by Internships


Call:
lm(formula = formula_interest, data = df)

Residuals:
   Min     1Q Median     3Q    Max 
-40735  -6125   -438   5528 108379 

Coefficients:
                                               Estimate Std. Error t value
(Intercept)                                   45656.640   8317.748   5.489
survey_internships1                            3604.936   1011.826   3.563
survey_internships2                            5837.802   1000.232   5.836
survey_internships3                            7541.957   1140.991   6.610
survey_internships4                            7406.342   2053.740   3.606
survey_internships5                            7552.596   3926.439   1.924
survey_stateIL                                 3692.104    639.600   5.773
survey_stateOther                              4219.424    644.808   6.544
survey_stateUnknown                            3134.314   1344.771   2.331
major1Business Analytics                       6045.129   1984.164   3.047
major1Business Economics                       2887.437   1431.287   2.017
major1Entrepreneurship                        -6082.486   3209.615  -1.895
major1Finance                                  3010.297    875.810   3.437
major1Human Capital Mgmt& Leadership          -4440.373   1822.688  -2.436
major1Information Systems                      7222.134   1356.786   5.323
major1Management and Leadership               -2306.465   2094.020  -1.101
major1Marketing                               -5749.178    929.134  -6.188
major1Supply Chain & Operations Mgmt            188.145   1136.568   0.166
`Combined Bacc and Masters`                    -825.223   1151.210  -0.717
`Dean's List`                                  -672.548    685.842  -0.981
`First Generation College Stdnt`               -509.133   1010.712  -0.504
`FSB Scholars`                                  500.544   1734.161   0.289
`Honors Program`                                702.831   1869.680   0.376
`President's List`                               -6.991   1345.355  -0.005
`Cum Laude`                                    5045.039   2361.200   2.137
`Magna Cum Laude`                              6306.967   2534.733   2.488
`Summa Cum Laude`                              9180.678   2690.967   3.412
`University Honors`                            -405.174   2042.148  -0.198
`UniversityHonors w/Distinction`              -1496.390   3877.650  -0.386
minor1Arts Related                            -6136.234   2214.978  -2.770
minor1Business Analytics                      -1396.087   1931.856  -0.723
minor1Business Legal Studies                  -7108.372   5600.846  -1.269
minor1Economics                               -4106.630   2792.557  -1.471
minor1Education                               -5229.608   7722.571  -0.677
minor1Engineering/Science                       631.286   2671.908   0.236
minor1Entrepreneurship                         -646.780   2560.869  -0.253
minor1Health Related                          -9193.175  10877.860  -0.845
minor1Humanities                              -1246.316   1986.353  -0.627
minor1Information Security                      610.528   3291.322   0.185
minor1Information Systems                       687.629   2126.341   0.323
minor1Interactive Media Studies                -517.292   2226.551  -0.232
minor1International Business                  -2984.491   3537.945  -0.844
minor1Language                                -2706.328   2097.039  -1.291
minor1Mangement and Leadership                -1675.390   2172.781  -0.771
minor1Marketing                               -2967.478   2780.051  -1.067
minor1Math/Stat                                 671.404   4033.387   0.166
minor1Media Related                             148.384   4203.460   0.035
minor1No Minor                                -1366.015   1757.372  -0.777
minor1Political Science                         663.483   3039.468   0.218
minor1Sport Management                        -2971.458   2472.816  -1.202
minor1Supply Chain Management                 -1264.170   2497.980  -0.506
IPEDS.Race.EthnicityAsian                     -1408.696   7671.546  -0.184
IPEDS.Race.EthnicityBlack or African American  2739.443   7877.844   0.348
IPEDS.Race.EthnicityHispanic/Latino           -2176.909   7610.957  -0.286
IPEDS.Race.EthnicityMulti Racial              -2411.491   7653.818  -0.315
IPEDS.Race.EthnicityNon-Resident Alien        -2744.629   7858.120  -0.349
IPEDS.Race.EthnicityUnknown                   -1261.634   9232.693  -0.137
IPEDS.Race.EthnicityWhite                     -3903.562   7514.445  -0.519
GenderMale                                     -368.581    571.469  -0.645
GPA.Range2.50 - 2.99                           5970.222   2901.606   2.058
GPA.Range3.00 - 3.49                           9075.421   2799.000   3.242
GPA.Range3.50 - 4.00                           7641.114   3697.900   2.066
                                              Pr(>|t|)    
(Intercept)                                   4.67e-08 ***
survey_internships1                           0.000377 ***
survey_internships2                           6.40e-09 ***
survey_internships3                           5.16e-11 ***
survey_internships4                           0.000320 ***
survey_internships5                           0.054585 .  
survey_stateIL                                9.30e-09 ***
survey_stateOther                             7.97e-11 ***
survey_stateUnknown                           0.019886 *  
major1Business Analytics                      0.002350 ** 
major1Business Economics                      0.043817 *  
major1Entrepreneurship                        0.058255 .  
major1Finance                                 0.000602 ***
major1Human Capital Mgmt& Leadership          0.014948 *  
major1Information Systems                     1.16e-07 ***
major1Management and Leadership               0.270859    
major1Marketing                               7.67e-10 ***
major1Supply Chain & Operations Mgmt          0.868541    
`Combined Bacc and Masters`                   0.473579    
`Dean's List`                                 0.326924    
`First Generation College Stdnt`              0.614513    
`FSB Scholars`                                0.772895    
`Honors Program`                              0.707032    
`President's List`                            0.995855    
`Cum Laude`                                   0.032773 *  
`Magna Cum Laude`                             0.012936 *  
`Summa Cum Laude`                             0.000661 ***
`University Honors`                           0.842752    
`UniversityHonors w/Distinction`              0.699619    
minor1Arts Related                            0.005662 ** 
minor1Business Analytics                      0.469987    
minor1Business Legal Studies                  0.204561    
minor1Economics                               0.141599    
minor1Education                               0.498383    
minor1Engineering/Science                     0.813254    
minor1Entrepreneurship                        0.800637    
minor1Health Related                          0.398161    
minor1Humanities                              0.530458    
minor1Information Security                    0.852863    
minor1Information Systems                     0.746444    
minor1Interactive Media Studies               0.816311    
minor1International Business                  0.399033    
minor1Language                                0.197040    
minor1Mangement and Leadership                0.440769    
minor1Marketing                               0.285938    
minor1Math/Stat                               0.867814    
minor1Media Related                           0.971844    
minor1No Minor                                0.437089    
minor1Political Science                       0.827231    
minor1Sport Management                        0.229671    
minor1Supply Chain Management                 0.612870    
IPEDS.Race.EthnicityAsian                     0.854329    
IPEDS.Race.EthnicityBlack or African American 0.728079    
IPEDS.Race.EthnicityHispanic/Latino           0.774896    
IPEDS.Race.EthnicityMulti Racial              0.752748    
IPEDS.Race.EthnicityNon-Resident Alien        0.726929    
IPEDS.Race.EthnicityUnknown                   0.891325    
IPEDS.Race.EthnicityWhite                     0.603499    
GenderMale                                    0.519035    
GPA.Range2.50 - 2.99                          0.039788 *  
GPA.Range3.00 - 3.49                          0.001209 ** 
GPA.Range3.50 - 4.00                          0.038951 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 10570 on 1663 degrees of freedom
Multiple R-squared:  0.2484,    Adjusted R-squared:  0.2208 
F-statistic: 9.009 on 61 and 1663 DF,  p-value: < 2.2e-16